/*
 * @lc app=leetcode.cn id=36 lang=java
 *
 * [36] 有效的数独
 *
 * https://leetcode-cn.com/problems/valid-sudoku/description/
 *
 * algorithms
 * Medium (63.75%)
 * Likes:    735
 * Dislikes: 0
 * Total Accepted:    232.4K
 * Total Submissions: 364.7K
 * Testcase Example:  '[["5","3",".",".","7",".",".",".","."],["6",".",".","1","9","5",".",".","."],[".","9","8",".",".",".",".","6","."],["8",".",".",".","6",".",".",".","3"],["4",".",".","8",".","3",".",".","1"],["7",".",".",".","2",".",".",".","6"],[".","6",".",".",".",".","2","8","."],[".",".",".","4","1","9",".",".","5"],[".",".",".",".","8",".",".","7","9"]]'
 *
 * 请你判断一个 9 x 9 的数独是否有效。只需要 根据以下规则 ，验证已经填入的数字是否有效即可。
 * 
 * 
 * 数字 1-9 在每一行只能出现一次。
 * 数字 1-9 在每一列只能出现一次。
 * 数字 1-9 在每一个以粗实线分隔的 3x3 宫内只能出现一次。（请参考示例图）
 * 
 * 
 * 
 * 
 * 注意：
 * 
 * 
 * 一个有效的数独（部分已被填充）不一定是可解的。
 * 只需要根据以上规则，验证已经填入的数字是否有效即可。
 * 空白格用 '.' 表示。
 * 
 * 
 * 
 * 
 * 示例 1：
 * 
 * 
 * 输入：board = 
 * [["5","3",".",".","7",".",".",".","."]
 * ,["6",".",".","1","9","5",".",".","."]
 * ,[".","9","8",".",".",".",".","6","."]
 * ,["8",".",".",".","6",".",".",".","3"]
 * ,["4",".",".","8",".","3",".",".","1"]
 * ,["7",".",".",".","2",".",".",".","6"]
 * ,[".","6",".",".",".",".","2","8","."]
 * ,[".",".",".","4","1","9",".",".","5"]
 * ,[".",".",".",".","8",".",".","7","9"]]
 * 输出：true
 * 
 * 
 * 示例 2：
 * 
 * 
 * 输入：board = 
 * [["8","3",".",".","7",".",".",".","."]
 * ,["6",".",".","1","9","5",".",".","."]
 * ,[".","9","8",".",".",".",".","6","."]
 * ,["8",".",".",".","6",".",".",".","3"]
 * ,["4",".",".","8",".","3",".",".","1"]
 * ,["7",".",".",".","2",".",".",".","6"]
 * ,[".","6",".",".",".",".","2","8","."]
 * ,[".",".",".","4","1","9",".",".","5"]
 * ,[".",".",".",".","8",".",".","7","9"]]
 * 输出：false
 * 解释：除了第一行的第一个数字从 5 改为 8 以外，空格内其他数字均与 示例1 相同。 但由于位于左上角的 3x3 宫内有两个 8 存在,
 * 因此这个数独是无效的。
 * 
 * 
 * 
 * 提示：
 * 
 * 
 * board.length == 9
 * board[i].length == 9
 * board[i][j] 是一位数字（1-9）或者 '.'
 * 
 * 
 */

// @lc code=start
class Solution {
    public boolean isValidSudoku(char[][] board) {
        boolean ret = true;
        // 初始化一个标记数组，有三层，分别对应9行，9列，9个块
        int[][][] mark = new int[3][9][9];
        // 循环标签
        check:
        for (int i = 0; i < board.length; i++) {
            for (int j = 0; j < board[i].length; j++) {
                if (board[i][j] != '.') {
                    int num = board[i][j] - '0' - 1;
                    mark[0][i][num]++;
                    mark[1][num][j]++;
                    // 将数独分为9块
                    // 0  1  2
                    // 3  4  5
                    // 6  7  8
                    // j/3代表块在第几行，i/3代表块在第几列
                    // 因此 (j/3)*3 + i/3可算得块数
                    int block = (j/3)*3 + i/3;
                    mark[2][block][num]++;
                    if (mark[0][i][num] > 1 || mark[1][num][j] > 1 ||mark[2][block][num] > 1) {
                        ret = false;
                        // 带标签的break语句直接跳出标签标记的循环
                        break check;
                    }
                }
            }
        }
        return ret;
    }
}
// @lc code=end

